 Percent Error
 Scientific Notation
Significant Figures (rarely used)
Formulation (simple first semester algebra)
Percent Error
% Error = |Accepted value – Experimental value| x 100
Accepted value
A student estimated the mass of an object as 250 g.
Experimental evidence confirmed that the object had a mass
of 240 g. Calculate the percent error of the estimation.
Solution
STEP 1: Identify all
information in the problem
Estimated mass
Experimental mass
Percent error
250 g
240 g
X
A student estimated the mass of an object as 250 g.
Experimental evidence confirmed that the object had a mass
of 240 g. Calculate the percent error of the estimation.
Solution
STEP 2: Identify formula to
use in problem…
% Error = |Accepted value – Experimental value| x 100
Accepted value
A student estimated the mass of an object as 250 g.
Experimental evidence confirmed that the object had a mass
of 240 g. Calculate the percent error of the estimation.
Solution
STEP 3: Substitute into
formula & solve…
X= |250 g – 240 g| x 100
250 g
X = 4.0 %
Percent Error
% Error = |Accepted value – Experimental value| x 100
Accepted value
Problem Solving
Method in Math
1. Identify given
information.
2. Identify formula
for problem.
3. Substitute into
formula and
solve.
Scientific Notation
A method of representing extremely large
and extremely small numbers.
Examples of Scientific Notation…
358,490,000,000,000,000,000,000,000,000,000
3.60 x 1032
0.000000000000000345
3.45 x 10-16
1.0 x 101
1.0 x 10 -1
10.0
0.10
1. Find the decimal and move it
until you get to a number
between 1-9.999.
2. Insert a “X” after the new
number.
3. Insert 10 after “X”.
4. Insert the number of places you
had to move the decimal as an
exponent to the “10”.
5. The exponent will be positive if
you had to move decimal toward
the left; negative if you had to
move decimal to the right.
Method for Scientific
Notation…
Scientific Notation Practice
Standard Notation
Scientific Notation
99.65
?
?
2.35 x 10-9
?
1.22 x 1012
0.000074
?
Significant Figures
Determines the accuracy of numbers used in labs
and calculations.
Sig Fig Rules…
1. ALL non-zero numbers are ALWAYS
significant.
1, 2, 3, 4, 5, 6, 7, 8, 9
Sig Fig Rules…
2. ALL zeros between non-zero numbers are
ALWAYS significant.
3005
Sig Fig Rules…
3. ALL zeroes BOTH to the right of the decimal
AND at the end of the number are ALWAYS
significant.
8.1000
Sig Fig Rules…
4. ALL zeroes to the left of the decimal AND in a
number ≥ 10 are ALWAYS significant.
3,000,000
10.0
Determine the number of significant figures in
each number.
1.205
2000
48.958
10.8
900.06
0.258
0.580000
0.0012
0.00008
800005
Basic Math & Sig Figs
Calculate:
4.6
+ 3.56
Calculate:
21.345
– 4.12
Calculate:
88.1
x 3.19
Calculate:
75.0___
5.2
Dimensional Analysis
A method of converting between various
measurements.
Dimensional Analysis
Example: How many seconds are there in a year?
Step 1: Break problem down into smaller problems
you can solve.
Small problem 1: How many seconds
in a minute?
1 minute = 60
seconds
Dimensional Analysis
Example: How many seconds are there in a year?
Step 1: Break problem down into smaller problems
1 minute = 60 seconds
you can solve.
Small problem 2: How many minutes
in an hour?
1 hour = 60 minutes
Dimensional Analysis
Example: How many seconds are there in a year?
Step 1: Break problem down into smaller problems
1 minute = 60 seconds
you can solve.
1 hour = 60 minutes
Small problem 3: How many hours in
a day?
1 day = 24 hours
Dimensional Analysis
Example: How many seconds are there in a year?
Step 1: Break problem down into smaller problems
1 minute = 60 seconds
you can solve.
1 hour = 60 minutes
1 day = 24 hours
Small problem 4: How many days in a
year?
1 year = 365 days
Dimensional Analysis
Example: How many seconds are there in a year?
Step 1: Break problem down into smaller problems
you can solve.
1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 year = 365 days
Dimensional Analysis
Example: How many seconds are there in a year?
Step 2: Arrange small problems in a table. Goal is
to cancel out time units (not numbers).
1 year
day
year
hour
day
minute
hour
second
minute
Dimensional Analysis
Example: How many seconds are there in a year?
Step 3: Insert appropriate values into boxes.
1 year
365 day
1 year
24 hour
1 day
60 minute
1 hour
60 second
1minute
Dimensional Analysis
Example: How many seconds are there in a year?
Step 4: Numbers on top are multiplied; on bottom
are divided.
1 year
365 day
1 year
24 hour
1 day
60 minute
1 hour
60 second
1minute
Dimensional Analysis
Example: How many seconds are there in a year?
1 x 365 x 24 x 60 x 60 = 31,536,000 seconds
Dimensional Analysis Practice
How many
meters in 1
kilometer?
How many
centimeters in
100 meters?
How many
How many
hours are there milliliters are
in 7.3 months? there in 3.6
liters?